The Math of Cat in the Hat: Would Cat Z Be Too Small to See?
Of course you’ve heard of Cat in the Hat. It’s a classic from Dr. Seuss. Well, there’s more than one book. In the second book (The Cat in the Hat Comes Back!), the Cat removes his hat to reveal a smaller cat — Cat A. Oh, but Cat A has a hat with an even smaller Cat B. This goes on and on in the classic manner of the whacky Cat. He claims there is a Cat Z.
So of course, the goal is to estimate the size of Cat Z. Let’s do it.
Measurements From the Book
Using a scan from the book, I can look at the size of the Cat and of Cat A. I’m going to use distances in pixels (at least for now). Here’s a rough estimates of the length of the two heads.
Instead of using pixels for sizes, I’m going to use the length of the main Cat. Let’s say that the Cat has a length of 1 c. If Cat A has the same proportions, then the ratios of heads would be the ratios of total sizes.
Now, let’s say The Cat is 1.5 meters tall. That means that I can find the height of Cat-A with a height of 0.555 meters. Well, now it’s time for even MORE data. Let’s just jump ahead in the story. Of course The Cat takes things to extreme and reveals more and more cats in hats. I can repeat the process using the following images.
